# Probability and quanta: why back to Nelson?

Banach Center Publications (1998)

- Volume: 43, Issue: 1, page 191-199
- ISSN: 0137-6934

## Access Full Article

top## Abstract

top## How to cite

topGarbaczewski, Piotr. "Probability and quanta: why back to Nelson?." Banach Center Publications 43.1 (1998): 191-199. <http://eudml.org/doc/208838>.

@article{Garbaczewski1998,

abstract = {We establish circumstances under which the dispersion of passive contaminants in a forced flow can be consistently interpreted as a Markovian diffusion process.},

author = {Garbaczewski, Piotr},

journal = {Banach Center Publications},

keywords = {diffusion processes; partial differential equations; stochastic mechanics},

language = {eng},

number = {1},

pages = {191-199},

title = {Probability and quanta: why back to Nelson?},

url = {http://eudml.org/doc/208838},

volume = {43},

year = {1998},

}

TY - JOUR

AU - Garbaczewski, Piotr

TI - Probability and quanta: why back to Nelson?

JO - Banach Center Publications

PY - 1998

VL - 43

IS - 1

SP - 191

EP - 199

AB - We establish circumstances under which the dispersion of passive contaminants in a forced flow can be consistently interpreted as a Markovian diffusion process.

LA - eng

KW - diffusion processes; partial differential equations; stochastic mechanics

UR - http://eudml.org/doc/208838

ER -

## References

top- [1] Ph. Blanchard and P. Garbaczewski, Natural boundaries for the Smoluchowski equation and affiliated diffusion processes, Phys. Rev. E 49, (1994), 3815.
- [2] K. L. Chung and Z. Zhao, From Brownian Motion to Schrödinger Equation, Springer-Verlag, Berlin, 1995. Zbl0819.60068
- [3] M. Freidlin, Functional Integration and Partial Differential Equations, Princeton University Press, Princeton, 1985.
- [4] P. Garbaczewski, J. R. Klauder and R. Olkiewicz, Schrödinger problem, Lévy processes, and noise in relativistic quantum mechanics, Phys. Rev. E 51, (1995), 4114.
- [5] P. Garbaczewski and R. Olkiewicz, Feynman-Kac kernels in Markovian representations of the Schrödinger interpolating dynamics, J. Math. Phys. 37, (1996), 730. Zbl0869.60101
- [6] P. Garbaczewski, Schrödinger's interpolation problem through Feynman-Kac kernels, Acta Phys. Polon. B 27, (1996), 617. Zbl0966.82512
- [7] P.Garbaczewski and G. Kondrat, Burgers velocity fields and dynamical transport processes, Phys. Rev. Lett. 77, (1996), 2608.
- [8] P. Garbaczewski, G. Kondrat and R. Olkiewicz, Burgers flows as Markovian diffusion processes, Phys. Rev. E 55, (1997), 1401. Zbl0939.35201
- [9] W. Horsthemke and R. Lefever, Noise-Induced Transitions, Springer-Verlag, Berlin, 1984. Zbl0529.60085
- [10] C. Marchioro and M. Pulvirenti, Vortex methods in Two-Dimensional Fluid Dynamics, Lecture Notes in Physics 203, Springer-Verlag, Berlin, 1984. Zbl0545.76027
- [11] E. Nelson, Dynamical Theories of the Brownian Motion, Princeton University Press, Princeton, 1967. Zbl0165.58502
- [12] H. Spohn, Large Scale Dynamics of Interacting Particles, Springer-Verlag, Berlin, 1992. Zbl0742.76002
- [13] H. Risken, The Fokker-Planck Equation, Springer-Verlag, Berlin, 1989. Zbl0665.60084
- [14] E. Schrödinger, Relativistic electron, Ann. Inst. Henri Poincaré, 2, (1932), 269.
- [15] J. C. Zambrini, Variational processes and stochastic versions of mechanics, J. Math. Phys. 27, (1986), 3207. Zbl0623.60102

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.